IDEAS home Printed from https://ideas.repec.org/a/wly/apsmbi/v35y2019i3p908-920.html
   My bibliography  Save this article

Preventive maintenance for homogeneous and heterogeneous systems

Author

Listed:
  • Maxim Finkelstein
  • Gregory Levitin

Abstract

We consider optimal preventive maintenance for homogeneous and heterogeneous systems with major (critical) and minor (noncritical) failures. A major failure results in a replacement of a failed system, whereas minor failures can be minimally instantaneously repaired. Distinct from the homogeneous case, where the process of minimal repairs is the Poisson process, the process of minimal repairs in the heterogeneous case is the mixed Poisson process that does not possess the memoryless property. This enables considering the number of minimal repairs as the decision parameter for the corresponding optimal preventive maintenance policy. The proposed approach is theoretically justified, and the detailed illustrative numerical examples are presented.

Suggested Citation

  • Maxim Finkelstein & Gregory Levitin, 2019. "Preventive maintenance for homogeneous and heterogeneous systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 908-920, May.
  • Handle: RePEc:wly:apsmbi:v:35:y:2019:i:3:p:908-920
    DOI: 10.1002/asmb.2422
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/asmb.2422
    Download Restriction: no

    File URL: https://libkey.io/10.1002/asmb.2422?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vladimir Rykov & Olga Kochueva & Yaroslav Rykov, 2021. "Preventive Maintenance of the k -out-of- n System with Respect to Cost-Type Criterion," Mathematics, MDPI, vol. 9(21), pages 1-15, November.
    2. Vladimir Rykov & Olga Kochueva, 2023. "Preventive Maintenance of k -out-of- n System with Dependent Failures," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    3. Vladimir Rykov & Olga Kochueva & Elvira Zaripova, 2023. "Renewable k -Out-of- n System with the Component-Wise Strategy of Preventive System Maintenance," Mathematics, MDPI, vol. 11(9), pages 1-21, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gregory Levitin & Maxim Finkelstein, 2018. "Optimal Mission Abort Policy for Systems Operating in a Random Environment," Risk Analysis, John Wiley & Sons, vol. 38(4), pages 795-803, April.
    2. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort policy optimization for series systems with overlapping primary and rescue subsystems operating in a random environment," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    3. Ji Hwan Cha & Maxim Finkelstein, 2019. "New failure and minimal repair processes for repairable systems in a random environment," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 522-536, May.
    4. Maxim S. Finkelstein, 2008. "On systems with shared resources and optimal switching strategies," MPIDR Working Papers WP-2008-025, Max Planck Institute for Demographic Research, Rostock, Germany.
    5. Laniado Rodas, Henry, 2013. "Allocation policies of redundancies in two-parallel-series and two-series-parallel systems," DES - Working Papers. Statistics and Econometrics. WS ws132622, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2018. "Constructing a Markov process for modelling a reliability system under multiple failures and replacements," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 34-47.
    7. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    8. Levitin, Gregory & Finkelstein, Maxim, 2018. "Optimal mission abort policy for systems in a random environment with variable shock rate," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 11-17.
    9. Omid Shojaee & Majid Asadi & Maxim Finkelstein, 2021. "On Some Properties of $$\alpha $$ α -Mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1213-1240, November.
    10. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    11. Anders S. G. Andrae & Mengjun Xia & Jianli Zhang & Xiaoming Tang, 2016. "Practical Eco-Design and Eco-Innovation of Consumer Electronics—the Case of Mobile Phones," Challenges, MDPI, vol. 7(1), pages 1-19, February.
    12. Ji Hwan Cha & Maxim Finkelstein, 2020. "Is perfect repair always perfect?," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 90-104, March.
    13. Wang, Xiaolin & Li, Lishuai & Xie, Min, 2020. "An unpunctual preventive maintenance policy under two-dimensional warranty," European Journal of Operational Research, Elsevier, vol. 282(1), pages 304-318.
    14. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Mission abort policy balancing the uncompleted mission penalty and system loss risk," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 194-201.
    15. Hossein Nadeb & Hamzeh Torabi & Ali Dolati, 2018. "Ordering the smallest claim amounts from two sets of interdependent heterogeneous portfolios," Papers 1812.06166, arXiv.org.
    16. Cha, Ji Hwan & Finkelstein, Maxim, 2024. "Preventive maintenance for the constrained multi-attempt minimal repair," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    17. P-E Labeau & M-C Segovia, 2011. "Effective age models for imperfect maintenance," Journal of Risk and Reliability, , vol. 225(2), pages 117-130, June.
    18. Ting Li & James Anderson, 2013. "Shaping human mortality patterns through intrinsic and extrinsic vitality processes," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(12), pages 341-372.
    19. Ji Cha & Maxim S. Finkelstein, 2009. "Stochastically ordered subpopulations and optimal burn-in procedure," MPIDR Working Papers WP-2009-030, Max Planck Institute for Demographic Research, Rostock, Germany.
    20. Yevkin, Alexander & Krivtsov, Vasiliy, 2020. "A generalized model for recurrent failures prediction," Reliability Engineering and System Safety, Elsevier, vol. 204(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:apsmbi:v:35:y:2019:i:3:p:908-920. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1526-4025 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.